时空的差分结构是否从物理原理中得出结论?
1Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva 8410501, Israel.
Entropy (Basel, Switzerland)
|March 28, 2024
概括
这项研究质疑数学在科学中的不合理有效性,认为坎托尔的集合论不适合物理学. 然而,因果关系可以从物理原理来定义数学结构.
科学领域:
- 物理学的基础 物理学的基础
- 数学物理 数学物理
- 集合理论 集合理论
背景情况:
- 探讨了尤金·维格纳关于"数学在自然科学中的不合理有效性"的概念.
- 在物理的背景下,批判性地分析乔治·坎托尔 (Georg Cantor) 声称数学是"人类思想的自由创造".
- 突出了坎托尔电源集构造的局限性,以保护几何点社区.
研究的目的:
- 重新评估数学在自然科学中的有效性的基础.
- 为了调查物理原理,如因果关系,是否可以内在定义数学结构.
- 在物理学中探索因果关系,拓学和微分几何之间的关系.
主要方法:
- 在没有先验数学结构的集合上定义爱因斯坦因果关系.
- 应用 Shirota 定理来嵌入得到的拓空间.
- 分析从QJ到实线 (RJ) 的完成过程.
主要成果:
- 爱因斯坦因果关系在可计数的无限集合上定义了一个Tychonoff拓.
- 集合可以作为RJ的封闭子空间嵌入,这表明因果关系意味着可微分的结构.
- 从QJ到RJ的完成过程的实证可测性仍然是一个挑战.
结论:
- 坎托尔集合论的基础并不直接适用于物理学的几何要求.
- 物理因果关系为产生与科学相关的数学结构提供了一个潜在的原则.
- 建议因果关系与RJ可微分结构之间的联系,但需要不可测试的完成过程.
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